First, let’s define our terms: garage punk is North American. Groups round the world made similar music – snarling, howling teen angst, inspired by R&B and powered by guitars and organs – but true garage punk comes from the US and, in a very few instances (the Haunted, for example), Canada. It blurs at its beginning and its end – some of the early 60s frat-rock bands and the wilder rock’n’roll groups are, fundamentally, garage bands, while in the late 60s garage punk began to blur into psychedelia. (Look at the tracklisting for Lenny Kaye’s original Nuggets album, the record that codified garage punk and you’ll find an awful lot of music that would not now fit comfortably into the genre).

Here the limits are the golden years of garage punk, 1965 to 1967, and the common thread is a certain sneeriness. Kicking off, the greatest of all garage bands, the Sonics, from Tacoma in Washington. Given that they formed in 1960, and featured saxophone prominently, the Sonics had plenty in common with frat rock. But the attitude was pure garage: their songs were vicious and furious and delivered by singer Gerry Roslie in a voice that couldn’t have been further from Elvis, let alone Perry Como. 1965’s Psycho, their greatest song, is the ur-text of garage punk: a riff of brutal simplicity, some incredible screams, and a lyric that doesn’t so much ponder sexual frustration as treat it as something from a horror movie: “Baby, you’re driving me crazy/ I’m going out of my head/ And now I wish I was dead/ Psycho!”

You’re Gonna Miss Me became one of the early signposts of psychedelia, when Roky Erickson’s 13th Floor Elevators recorded it with Tommy Hall’s “electric jug” wobbling all over the top of it. In fact, Erickson had already recorded the song in 1965 with his previous band, the Spades. Admittedly, this version isn’t as unhinged as the Elevators’s take on the song, but it’s still an important record. Where the Sonics exemplified the Pacific northwestern garage sound – extrapolated from rock’n’roll and made for playing at school dances – the Spades, from Texas, showed the different way of doing things in the Lone Star State: less conventional, more dreamy, more obviously druggy (listen to the wordless backing vocals on the chorus and the heavily tremeloed lead guitar line). But some things are the same, whatever the state. Like Gerry Roslie, Roky’s upset about his girl: “I gave you the warning/ But you never heeded it/ How can you say you miss my loving/ When you never needed it?”

Link Wray was one of the forefathers of garage punk, thanks to a brutal guitar sound – his 1958 hit Rumble is credited with being the first record to feature power chords. Most of his recordings are instrumentals (the Shadows had a big UK hit with one, a cover of Apache), but this 1966 B-side shows him embracing the sound he’d helped spawn with a rare vocal. Wray had only one lung – he had the other removed after contracting tuberculosis while serving with the US Army during the Korean war and was told he would never sing again – which might account for the peculiarly enervated air of the vocal of Hidden Charms, on which he sounds like it’s an effort to force each line out. But that suits the song: for a 37-year-old, Wray is pretty convincing as a pent-up teenager, and he sings not like someone who can’t catch his breath but like a kid who’s perhaps been up to something unmentionable in his bedroom. “Well, your lips are sweet as honeydew/ I think about you, that’s all I do.” Of course he wants to get to her hidden charms. Who wouldn’t?

Barry Tashian was an Armenian-American kid in Boston who, his son Daniel (of the excellent Silver Seas) told me, was consumed by anger at the world. In part, perhaps, because Armenian-American kids may not have been top of the popularity scale in a town dominated by Irish-Americans and Wasps. He channelled the anger into music, leading the Remains into massive popularity in New England (they were chosen to open for the Beatles on their final tour in 1966). The Remains were, perhaps, a little too sophisticated to be a true garage band – they had proper arrangements and melodies, rather than just splurging their rage on to vinyl – but Don’t Look Back remains one of the most thrilling relics of mid-60s American rock, complete with a fabulous faux gospel breakdown: “I got one thing I gotta say … You know, people got some strange ideas about how life should be lived and things should be done/ But I’m here to say you gotta do just what you want!” Amen.

Garage punk had its standards – the Yardbirds’ version of I’m a Man, and rewrites thereof (such as the Count Five’s Psychotic Reaction or the Other Half’s Mr Pharmacist) was one of the commonest. I’m a Man had been written by Bo Diddley, and another of his songs was a staple, too. Who Do You Love’s lyrics always sounded like a nightmare, something conjured from a world beyond our normal experience: “I walked 47 miles of barbed wire/ I got a cobra snake for a necktie/ I got a brand new house by the roadside, made out of rattlesnake hide/ I got a brand-new chimney made on top, made out of human skulls … Got a tombstone hand and a graveyard mind/ I’m just 22 and I don’t mind dying.” But Diddley’s original sounds almost amiable compared to the Woolies’. While the Diddley beat comes in on the chorus, Stormy Rice’s snarled vocal and the fuzzed guitar and Farfisa organ combination on the verses make this version – a No 95 smash hit on the Billboard chart – sound like the work of a band who want to mug you, not hold your hand.

Dirty Wurds were Chicago teens who started out playing bluegrass, then went electric in imitation of Bob Dylan. They didn’t match Dylan for either musical or lyrical dexterity, though: the song has one of the most monolithic riffs in garage punk and a lyric whose sophistication would be decried by the average toddler: “I need your loving/ I need you very much/ I need your tender touch/ I love you very much.” But garage punk isn’t meant to be subtle or poetic; it’s meant to sound like the barbaric yawp of a furious teenager.

I Had Too Much to Dream (Last Night) and Get Me to the World on Time are the ones people know – crazy guys, crazy puns – but the standout on the first Prunes album, before they were taken over and turned into David Axelrod’s pet concept project, was this berserk R&B stomper, complete with what sounds awfully like that most ungarage of instruments, the marimba. The Prunes are one of the outliers of garage punk: they were signed to a major label, but not trusted to write their own songs. Then Axelrod took them over and replaced the members with session musicians for recording, only to discover this meant the actual band couldn’t play the music he’d made for them when it was time to play live. The Electric Prunes make the Monkees (whose Stepping Stone is a garage punk classic in its own right) look like an organically assembled band. But for Dream, World and Try Me they deserve to have their portraits in places of honour in garage Valhalla.

Texas in the 1960s was not the easiest place to be a freak, something Roky Erickson discovered that to his cost. As ZZ Top’s Dusty Hill told me a couple of years back: “Being a musician in Texas had its own set of risks – long hair, whatnot. I was with a group called the American Blues, and time we had long blue hair. In the 60s in Texas. I got probably less shit about having blue hair than about having long hair, because I believe they thought I was crazy.” His future bandmate Billy Gibbons had his own group, too, the Moving Sidewalks, who were inspired by Erickson and the Elevators.

Though much of the Sidewalks’ catalogue – well, album – doesn’t count as garage punk, their big hit single certainly does: riff, organ and sneer are all present and correct. Of course, the idea of a big hit single is all relative: 99th Floor was No 1 in Houston, the Sidewalks’ hometown, for six weeks, but this was in the days when acts could be huge locally and unknown 20 miles down the road. Gibbons has never lost touch with this music: the Sidewalks periodically reunite, with their frontman setting aside his ZZ Top fame to play with them, and Top themselves contributed a fabulous version of Reverberation (Doubt) to the 1990 Erickson tribute album Where the Pyramid Meets the Eye (the title comes from the answer Erickson gave when asked to define psychedelia).

One of garage punk’s set texts, covered countless times without ever losing its primal might, Action Woman is a bit of a mystery. Though this version is the best known by a massive distance, it may not be the first. The Litter were one of two Minnesota groups, along with the Electras, who worked with the writer of the song, Warren Kendrick. One Litter fansite asserts they recorded the song in November 1966, while the Electras didn’t get to the studio till spring 1967. Another garage site claims the Litter didn’t record their version till January 1967. Who knows? The tale of Action Woman is one of those marvellous flukes that 60s pop seemed to throw up at will, and which if it were made into a film now would be dismissed as too far-fetched.

Kendrick was a high school maths teacher who made a novelty record – Beer Bust Blues – in 1965, which gave him the music bug, and set him looking for bands to record. Yes, one of the most unhinged songs of the 60s was written by a maths teacher. The very thought that he might have been sitting there in front of a group of bored teens pondering his need to find “a satisfaction woman, before I lose my mind” is oddly chilling. For the record, the Electras’ version is even better, but is sadly unavailable on Spotify.

Let’s conclude with something from the point where garage starts tipping over into psychedelia. It’s from a band whose career lasted for just one recording session but who produced a song that was included on the original Nuggets compilation – and which granted them an afterlife that allows them to re-form and play garage festivals. I’m Five Years Ahead of My Time is almost a template of a garage psych piece: cack-handed attempts at modal melodies, a fuzzed and wah-wahed lead guitar line that’s meant to sound like a sitar, an instrumental wig out and a singer making preposterous claims about their own mental elevation: “Look into my head, look ahead don’t look behind/ I’m five years ahead of my time.” It’s magnificent, preposterous and undeniable. Most of all, like all great garage rock, it’s enormous fun.